What is the Greatest Common Factor of 76320 and 76338?

Greatest common factor (GCF) of 76320 and 76338 is 18.

GCF(76320,76338) = 18

We will now calculate the prime factors of 76320 and 76338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76320 and 76338.

How to find the GCF of 76320 and 76338?

We will first find the prime factorization of 76320 and 76338. After we will calculate the factors of 76320 and 76338 and find the biggest common factor number .

Step-1: Prime Factorization of 76320

Prime factors of 76320 are 2, 3, 5, 53. Prime factorization of 76320 in exponential form is:

76320 = 2⁵ × 3² × 5¹ × 53¹

Step-2: Prime Factorization of 76338

Prime factors of 76338 are 2, 3, 4241. Prime factorization of 76338 in exponential form is:

76338 = 2¹ × 3² × 4241¹

Step-3: Factors of 76320

List of positive integer factors of 76320 that divides 76320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 53, 60, 72, 80, 90, 96, 106, 120, 144, 159, 160, 180, 212, 240, 265, 288, 318, 360, 424, 477, 480, 530, 636, 720, 795, 848, 954, 1060, 1272, 1440, 1590, 1696, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 5088, 6360, 7632, 8480, 9540, 12720, 15264, 19080, 25440, 38160

Step-4: Factors of 76338

List of positive integer factors of 76338 that divides 76320 without a remainder.

1, 2, 3, 6, 9, 18, 4241, 8482, 12723, 25446, 38169

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76320 and 76338. The biggest common factor number is the GCF number.
So the greatest common factor 76320 and 76338 is 18.

Also check out the Least Common Multiple of 76320 and 76338